How to Calculate Margin of Error: Steps. Step 1: Find the critical value. The critical value is either a t-score or a z-score. If you aren’t sure, see: T-score vs z-score. In general, for small sample sizes (under 30) or when you don’t know the population standard deviation, use a t-score. Otherwise, use a z-score. The symbol α is the Greek letter alpha. It is related to the level of confidence that we are working with for our confidence interval. Any percentage less than 100% is possible for a level of confidence, but in order to have meaningful results, we need to use numbers close to 100%. Multiply the result by the appropriate z*-value for the confidence level desired. Refer to the above table for the appropriate z*-value.If the confidence level is 95%, the z*-value is 1.96. Here’s an example: Suppose that the Gallup Organization’s latest poll sampled 1,000 people from the United States, and the results show that 520 people (52%) think the president is doing a good job. margin of error, confidence interval, statistics. 1967 Shelby GT500 Barn Find and Appraisal That Buyer Uses To Pay Widow - Price Revealed - Duration: 22:15. Jerry Heasley Recommended for you 🚨 New polling by @SavantaComRes as part of UUK's 'fair admissions review' Findings: While the majority of students and recent graduates find the university admissions process to be fair, 28% disagree the current system works well Get the population standard deviation (σ) and sample size (n). Take the square root of your sample size and divide it into your population standard deviation is the population standard deviation, n is the sample size, and z* is the appropriate z*-value for your desired level of confidence (which you can find in the following table). By using margin of error, readers are able to get a clearer idea of what the numbers actually mean. Understand the results of the poll. Examine all the factors, including population size, sample size and standard deviation. Suppose that we are working with a 95% level of confidence. We want to look up the z-score z*for which the area between -z* and z* is 0.95.From the table, we see that this critical value is 1.96.